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1 CMS / EPSRC – Steve Babbage C1 - Unrestricted
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25th March 2009
Group R&D
Some maths from the telecommunications industry
Presented by Dr Steve Babbage
25 March 2009
CMS / EPSRC – Steve Babbage2 C1 - Unrestricted
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Purpose of this presentation
To illustrate some industrial applications that require and inspire mathematical research
• Optimisation
• Data security
And underpinning both of those:
• Complexity
3 CMS / EPSRC – Steve Babbage C1 - Unrestricted
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Optimisation
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Frequency planning
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Frequency planning
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Frequency planning
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Frequency planning
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Site selection
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Radial network planning
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Mesh network planning
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Traffic scheduling / queueing
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Traffic routing
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Multi-layered networks
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Cryptography and data security
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Types of encryption algorithm
Steve Babbage
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Block ciphers and stream ciphers
Key (128 bits)
Plaintext (128 bits)
Ciphertext (128 bits)
Key
Plaintext
Key (128 bits)
011101110100101101 ...
Plaintext (any length)
101011011101001110 ...
Ciphertext 110110101001100011 ...
=
Key (128 bits)
011101110100101101 ...
=Plaintext 101011011101001110 ...
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Digital signature
Steve BabbageThis is an extremely long
document which could go on for pages and pages and
pages and pages and pages and pages and pages and
pages and pages and pages and pages and pages and
pages and pages and pages and pages and pages and
pages and pages and pages
5A90CB3820FB2744E11C49572C0D3919
Hash function
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Theory – and lack of theory
Block ciphers
• Linear cryptanalysis
• Differential cryptanalysis
Hash functions
• ???
Lots of insight still needed
Symmetric ciphers
• Algebraic cryptanalysis– Gröbner bases
Public key algorithms
• Factoring
• Discrete logarithm
• Elliptic curve
• Others
Quantum computers
• What can they do?
• What can't they do?
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Complexity
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Closing thoughts
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Thanks to:
• Terry Lyons – Oxford / WIMCS
• Bart Preneel – Leuven
• Robert Leese – Oxford / Smith Institute
• Peter Grindrod – Reading
• John McWhirter – Cardiff
Thank you
Further input taken from:
• Zuse Institute Berlin
